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<div class="title">dynamical_systems.hpp</div>  </div>
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<a href="dynamical__systems_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#pragma once</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &lt;math.h&gt;</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &lt;Eigen/Eigen&gt;</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="basic__tools_8hpp.html">mpi_cpp_tools/basic_tools.hpp</a>&quot;</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="math_8hpp.html">mpi_cpp_tools/math.hpp</a>&quot;</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacemct.html">mct</a></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;{</div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;</div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;</div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;</div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div><div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="classmct_1_1LinearDynamics.html">   28</a></span>&#160;<span class="keyword">class </span><a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a></div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;{</div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keyword">typedef</span> Eigen::Matrix&lt;double, Eigen::Dynamic, 1, 0, 10&gt; Vector;</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a>(Eigen::Vector4d parameters): <a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a>(parameters[0],</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                                                parameters[1],</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;                                                parameters[2],</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;                                                parameters[3]) { }</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a>(<span class="keywordtype">double</span> jerk,</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                   <span class="keywordtype">double</span> initial_acceleration,</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                   <span class="keywordtype">double</span> initial_velocity,</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                   <span class="keywordtype">double</span> initial_position)</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    {</div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        jerk_ = jerk;</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        initial_acceleration_ = initial_acceleration;</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        initial_velocity_ = initial_velocity;</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        initial_position_= initial_position;</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    }</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keywordtype">double</span> get_acceleration(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        <span class="keywordflow">return</span>  jerk_ * t +</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                initial_acceleration_;</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    }</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keywordtype">double</span> get_velocity(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <span class="keywordflow">return</span> jerk_ * 0.5 * t * t +</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;                initial_acceleration_ * t +</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                initial_velocity_;</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    }</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordtype">double</span> get_position(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keywordflow">return</span> jerk_ * 0.5 * 1./3. * t * t * t +</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;                initial_acceleration_ * 0.5 * t * t +</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;                initial_velocity_ * t +</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                initial_position_;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    }</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    Vector find_t_given_velocity(<span class="keywordtype">double</span> velocity)<span class="keyword"> const</span></div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keywordtype">double</span> a = jerk_ * 0.5;</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <span class="keywordtype">double</span> b = initial_acceleration_;</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="keywordtype">double</span> c = initial_velocity_ - velocity;</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        <span class="keywordtype">double</span> determinant = b * b - 4 * a * c;</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        Vector solutions(Vector::Index(0));</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="keywordflow">if</span>(a == 0)</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        {</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <span class="keywordflow">if</span>(b != 0)</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;            {</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                solutions.resize(1);</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                solutions[0] = - c / b;</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;            }</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        }</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(determinant == 0)</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        {</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            solutions.resize(1);</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            solutions[0] = -b / 2 / a;</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        }</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(determinant &gt; 0)</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        {</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="keywordtype">double</span> determinant_sqrt = std::sqrt(determinant);</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            solutions.resize(2);</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;            solutions[0] = (-b + determinant_sqrt) / 2 / a;</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            solutions[1] = (-b - determinant_sqrt) / 2 / a;</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        }</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        Vector positive_solutions(Vector::Index(0));</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; solutions.size(); i++)</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        {</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;            <span class="keywordflow">if</span>(solutions[i] &gt;= 0)</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;            {</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                mct::append_to_vector(positive_solutions, solutions[i]);</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;            }</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        }</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        <span class="keywordflow">return</span> positive_solutions;</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    }</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="keyword">protected</span>:</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordtype">double</span> jerk_;</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    <span class="keywordtype">double</span> initial_acceleration_;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="keywordtype">double</span> initial_velocity_;</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="keywordtype">double</span> initial_position_;</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;};</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;</div><div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">  123</a></span>&#160;<span class="keyword">class </span><a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a>: <span class="keyword">public</span> <a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a></div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;{</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keywordtype">void</span> print_parameters()<span class="keyword"> const</span></div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;-------------------------------------------&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;jerk: &quot;</span> &lt;&lt; jerk_ &lt;&lt; std::endl</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;initial_acceleration: &quot;</span> &lt;&lt; initial_acceleration_ &lt;&lt; std::endl</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;initial_velocity: &quot;</span> &lt;&lt; initial_velocity_ &lt;&lt; std::endl</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;initial_position: &quot;</span> &lt;&lt; initial_position_ &lt;&lt; std::endl</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;acceleration_limit: &quot;</span> &lt;&lt; acceleration_limit_ &lt;&lt; std::endl</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;jerk_duration: &quot;</span> &lt;&lt; jerk_duration_ &lt;&lt; std::endl;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;-------------------------------------------&quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    }</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;</div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keyword">typedef</span> LinearDynamics::Vector Vector;</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    <span class="keyword">typedef</span> Eigen::Matrix&lt;double, Eigen::Dynamic, Eigen::Dynamic, 0, 10, 10&gt;</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    Matrix;</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a>(Eigen::Matrix&lt;double, 5, 1&gt; parameters):</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a>(parameters[0],</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        parameters[1],</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        parameters[2],</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        parameters[3],</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        parameters[4]) { }</div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a>(<span class="keywordtype">double</span> jerk,</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;                                             <span class="keywordtype">double</span> initial_acceleration,</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;                                             <span class="keywordtype">double</span> initial_velocity,</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                                             <span class="keywordtype">double</span> initial_position,</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;                                             <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> abs_acceleration_limit):</div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <a class="code" href="classmct_1_1LinearDynamics.html">LinearDynamics</a>(jerk,</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                       initial_acceleration,</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                       initial_velocity,</div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                       initial_position)</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    {</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="keywordflow">if</span>(jerk_ &gt; 0)</div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;            acceleration_limit_ = abs_acceleration_limit;</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        <span class="keywordflow">else</span></div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            acceleration_limit_ = -abs_acceleration_limit;</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        set_initial_acceleration(initial_acceleration);</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    }</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keywordtype">void</span> set_initial_acceleration(<span class="keywordtype">double</span> initial_acceleration)</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    {</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <span class="keywordflow">if</span>(std::fabs(initial_acceleration) &gt; std::fabs(acceleration_limit_))</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">&quot;expected &quot;</span></div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;                                        <span class="stringliteral">&quot;std::fabs(initial_acceleration) &gt; &quot;</span></div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;                                        <span class="stringliteral">&quot;abs_acceleration_limit&quot;</span>);</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        initial_acceleration_ = initial_acceleration;</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        jerk_duration_ =</div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;                (acceleration_limit_ - initial_acceleration_) / jerk_;</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    }</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    <span class="keywordtype">double</span> get_acceleration(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;        <span class="keywordflow">if</span>(t &lt; jerk_duration_)</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        {</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;            <span class="keywordflow">return</span>  LinearDynamics::get_acceleration(t);</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        }</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;        <span class="keywordflow">else</span></div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        {</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;            <span class="keywordflow">return</span> acceleration_limit_;</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        }</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    }</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    <span class="keywordtype">double</span> get_velocity(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keywordflow">if</span>(t &lt; jerk_duration_)</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        {</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            <span class="keywordflow">return</span> LinearDynamics::get_velocity(t);</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        }</div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        <span class="keywordflow">else</span></div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        {</div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;            <span class="keywordflow">return</span> LinearDynamics::get_velocity(jerk_duration_) +</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                    acceleration_limit_ * (t - jerk_duration_);</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;        }</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    }</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordtype">double</span> get_position(<a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> t)<span class="keyword"> const</span></div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;        <span class="keywordflow">if</span>(t &lt; jerk_duration_)</div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        {</div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;            <span class="keywordflow">return</span> LinearDynamics::get_position(t);</div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;        }</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;        <span class="keywordflow">else</span></div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;        {</div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;            <span class="keywordflow">return</span> LinearDynamics::get_position(jerk_duration_) +</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                    LinearDynamics::get_velocity(jerk_duration_) * (t - jerk_duration_) +</div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                    acceleration_limit_ * 0.5 * (t - jerk_duration_) * (t - jerk_duration_);</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        }</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    }</div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;</div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Array&gt;</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    Array get_positions(<span class="keyword">const</span> Array&amp; times)<span class="keyword"> const</span></div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;        Array positions(times.size());</div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; times.size(); i++)</div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;        {</div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;            positions[i] = get_position(times[i]);</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        }</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        <span class="keywordflow">return</span> positions;</div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    }</div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    Vector find_t_given_velocity(<span class="keywordtype">double</span> velocity)<span class="keyword"> const</span></div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        Vector potential_solutions =</div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;                LinearDynamics::find_t_given_velocity(velocity);</div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;</div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;        Vector solutions(Vector::Index(0));</div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; potential_solutions.size(); i++)</div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;        {</div><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;            <span class="keywordflow">if</span>(potential_solutions[i] &lt;= jerk_duration_)</div><div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;            {</div><div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;                mct::append_to_vector(solutions, potential_solutions[i]);</div><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            }</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        }</div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;</div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;        <span class="keywordtype">double</span> potential_solution = jerk_duration_</div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                + (velocity - LinearDynamics::get_velocity(jerk_duration_))</div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;                / acceleration_limit_;</div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;        <span class="keywordflow">if</span>(potential_solution &gt; jerk_duration_ &amp;&amp;</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;                !(mct::contains(solutions, jerk_duration_) &amp;&amp;</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;                  mct::approx_equal(potential_solution, jerk_duration_)))</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        {</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;            mct::append_to_vector(solutions, potential_solution);</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        }</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;</div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;        <span class="keywordflow">if</span>(solutions.size() &gt; 2)</div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;        {</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;too many solutions, something went wrong!!!&quot;</span></div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;                      &lt;&lt; std::endl;</div><div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;            print_parameters();</div><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;</div><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;potential_solutions[0]: &quot;</span> &lt;&lt; potential_solutions[0] &lt;&lt; std::endl;</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;potential_solutions size: &quot;</span> &lt;&lt; potential_solutions.size() &lt;&lt; <span class="stringliteral">&quot; content: &quot;</span> &lt;&lt; potential_solutions.transpose() &lt;&lt; std::endl;</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;solutions size: &quot;</span> &lt;&lt; solutions.size() &lt;&lt; <span class="stringliteral">&quot; content: &quot;</span> &lt;&lt; solutions.transpose() &lt;&lt; std::endl;</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;            exit(-1);</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        }</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="keywordflow">return</span> solutions;</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    }</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keywordtype">bool</span> will_exceed_jointly(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_velocity,</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;                             <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_position)<span class="keyword"> const</span></div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        <span class="keywordtype">double</span> certificate_time;</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        <span class="keywordflow">return</span> will_exceed_jointly(max_velocity, max_position, certificate_time);</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    }</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;</div><div class="line"><a name="l00281"></a><span class="lineno"><a class="line" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html#a568991a3b2459be274a86298caf8356c">  281</a></span>&#160;    <span class="keywordtype">bool</span> <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html#a568991a3b2459be274a86298caf8356c">will_exceed_jointly</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_velocity,</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;                             <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_position,</div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;                             <span class="keywordtype">double</span>&amp; certificate_time)<span class="keyword"> const</span></div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        <span class="keywordflow">if</span>(max_velocity == std::numeric_limits&lt;double&gt;::infinity() ||</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;                max_position == std::numeric_limits&lt;double&gt;::infinity())</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        {</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;        }</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        <span class="keywordflow">if</span>(jerk_ &gt; 0)</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        {</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;            certificate_time = std::numeric_limits&lt;double&gt;::infinity();</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        }</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;        <span class="keywordflow">if</span>(jerk_ == 0)</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;        {</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;            <span class="keywordflow">throw</span> std::domain_error(<span class="stringliteral">&quot;not implemented for jerk == 0&quot;</span>);</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;        }</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;        <span class="comment">// find maximum achieved position --------------------------------------</span></div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="comment"></span>        <span class="comment">//        Matrix candidate_points(0, 0);</span></div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;        <span class="comment">//        Vector candidate_times(0);</span></div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;        <span class="comment">//        mct::append_rows_to_matrix(candidate_points,</span></div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;        <span class="comment">//                              Eigen::Vector2d(initial_velocity_,</span></div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;        <span class="comment">//                                              initial_position_).transpose());</span></div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;        <span class="comment">//        mct::append_to_vector(candidate_times, 0);</span></div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;</div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;</div><div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;        <span class="keywordflow">if</span>(initial_velocity_ &gt; max_velocity &amp;&amp;</div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;                initial_position_ &gt; max_position)</div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;        {</div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;            certificate_time = 0;</div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;        }</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;        Vector t_given_zero_velocity = find_t_given_velocity(0);</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;        <span class="keywordflow">if</span>(t_given_zero_velocity.size() &gt; 0)</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;        {</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;            Vector position_given_zero_velocity =</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;                    get_positions(t_given_zero_velocity);</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;</div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;            Vector::Index max_index;</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;            <span class="keywordtype">double</span> max_achieved_position =</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;                    position_given_zero_velocity.maxCoeff(&amp;max_index);</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;            <span class="keywordflow">if</span>(max_achieved_position &lt; max_position)</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;            {</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;            }</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;            <span class="keywordflow">if</span>(max_velocity &lt; 0)</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;            {</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;                certificate_time = t_given_zero_velocity[max_index];</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;            }</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        }</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        Vector t_given_max_velocity =</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;                find_t_given_velocity(max_velocity);</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;        Vector position_given_max_velocity =</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;                get_positions(t_given_max_velocity);</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;</div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; position_given_max_velocity.size(); i++)</div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;        {</div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;            <span class="keywordflow">if</span>(position_given_max_velocity[i] &gt; max_position)</div><div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;            {</div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;                certificate_time = t_given_max_velocity[i];</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;            }</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        }</div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;</div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    }</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;</div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    <span class="keywordtype">bool</span> will_deceed_jointly(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_velocity,</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;                             <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_position)<span class="keyword"> const</span></div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        <span class="keywordtype">double</span> certificate_time;</div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        <span class="keywordflow">return</span> will_deceed_jointly(min_velocity, min_position, certificate_time);</div><div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    }</div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <span class="keywordtype">bool</span> will_deceed_jointly(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_velocity,</div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;                             <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_position,</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;                             <span class="keywordtype">double</span>&amp; certificate_time)<span class="keyword"> const</span></div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;<span class="keyword">    </span>{</div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;        <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a></div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;                flipped_dynamics(-jerk_,</div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;                                 -initial_acceleration_,</div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;                                 -initial_velocity_,</div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;                                 -initial_position_,</div><div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;                                 std::fabs(acceleration_limit_));</div><div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;</div><div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;        <span class="keywordflow">return</span> flipped_dynamics.will_exceed_jointly(-min_velocity,</div><div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;                                                    -min_position,</div><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;                                                    certificate_time);</div><div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    }</div><div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;</div><div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;</div><div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="keyword">private</span>:</div><div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    <span class="keywordtype">double</span> acceleration_limit_;</div><div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> jerk_duration_;</div><div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;};</div><div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;</div><div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;</div><div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;</div><div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="dynamical__systems_8hpp.html#aab449f0863dee56d0f0e377c75a4812d">  387</a></span>&#160;<span class="keywordtype">double</span> <a class="code" href="dynamical__systems_8hpp.html#aab449f0863dee56d0f0e377c75a4812d">find_max_admissible_acceleration</a>(</div><div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; initial_velocity,</div><div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; initial_position,</div><div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_velocity,</div><div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; max_position,</div><div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;        <span class="keyword">const</span> <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a>&amp; abs_jerk_limit,</div><div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;        <span class="keyword">const</span> <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a>&amp; abs_acceleration_limit)</div><div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;{</div><div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    <span class="keywordtype">double</span> lower = -abs_acceleration_limit;</div><div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    <span class="keywordtype">double</span> upper = abs_acceleration_limit;</div><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;</div><div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;</div><div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <a class="code" href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">LinearDynamicsWithAccelerationConstraint</a> dynamics(-abs_jerk_limit,</div><div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;                                                      lower,</div><div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;                                                      initial_velocity,</div><div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;                                                      initial_position,</div><div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;                                                      abs_acceleration_limit);</div><div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;</div><div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;</div><div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    <span class="keywordflow">if</span>(dynamics.will_exceed_jointly(max_velocity, max_position))</div><div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    {</div><div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        <span class="keywordflow">return</span> lower;</div><div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    }</div><div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;</div><div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    dynamics.set_initial_acceleration(upper);</div><div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">if</span>(!dynamics.will_exceed_jointly(max_velocity, max_position))</div><div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    {</div><div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;        <span class="keywordflow">return</span> upper;</div><div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    }</div><div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;</div><div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 0; i &lt; 20; i++)</div><div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    {</div><div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        <span class="keywordtype">double</span> middle = (lower + upper) / 2.0;</div><div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;</div><div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        dynamics.set_initial_acceleration(middle);</div><div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;        <span class="keywordflow">if</span>(dynamics.will_exceed_jointly(max_velocity, max_position))</div><div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;        {</div><div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;            upper = middle;</div><div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;        }</div><div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;        <span class="keywordflow">else</span></div><div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;        {</div><div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;            lower = middle;</div><div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;        }</div><div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    }</div><div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    <span class="keywordflow">return</span> lower;</div><div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;}</div><div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;</div><div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;</div><div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;</div><div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;<span class="keywordtype">double</span> find_min_admissible_acceleration(</div><div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; initial_velocity,</div><div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; initial_position,</div><div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_velocity,</div><div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; min_position,</div><div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;        <span class="keyword">const</span> <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a>&amp; abs_jerk_limit,</div><div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;        <span class="keyword">const</span> <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a>&amp; abs_acceleration_limit)</div><div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;{</div><div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    <span class="keywordflow">return</span> -<a class="code" href="dynamical__systems_8hpp.html#aab449f0863dee56d0f0e377c75a4812d">find_max_admissible_acceleration</a>(-initial_velocity,</div><div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;                                             -initial_position,</div><div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;                                             -min_velocity,</div><div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;                                             -min_position,</div><div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;                                             abs_jerk_limit,</div><div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;                                             abs_acceleration_limit);</div><div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;}</div><div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;</div><div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;</div><div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;</div><div class="line"><a name="l00455"></a><span class="lineno"><a class="line" href="classmct_1_1SafetyConstraint.html">  455</a></span>&#160;<span class="keyword">class </span><a class="code" href="classmct_1_1SafetyConstraint.html">SafetyConstraint</a></div><div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;{</div><div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    <a class="code" href="classmct_1_1SafetyConstraint.html">SafetyConstraint</a>()</div><div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    {</div><div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;        min_velocity_ = -std::numeric_limits&lt;double&gt;::infinity();</div><div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;        min_position_ = -std::numeric_limits&lt;double&gt;::infinity();</div><div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;        max_velocity_ = std::numeric_limits&lt;double&gt;::infinity();</div><div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;        max_position_ = std::numeric_limits&lt;double&gt;::infinity();</div><div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;        max_torque_ = 1.0;</div><div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;        max_jerk_ = 1.0;</div><div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;        inertia_ = 1.0;</div><div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    }</div><div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;</div><div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    <a class="code" href="classmct_1_1SafetyConstraint.html">SafetyConstraint</a>(<span class="keywordtype">double</span> min_velocity,</div><div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;                     <span class="keywordtype">double</span> min_position,</div><div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;                     <span class="keywordtype">double</span> max_velocity,</div><div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;                     <span class="keywordtype">double</span> max_position,</div><div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;                     <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> max_torque,</div><div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;                     <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> max_jerk,</div><div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;                     <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> inertia)</div><div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    {</div><div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;        min_velocity_ = min_velocity;</div><div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;        min_position_ = min_position;</div><div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;        max_velocity_ = max_velocity;</div><div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;        max_position_ = max_position;</div><div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;        max_torque_ = max_torque;</div><div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;        max_jerk_ = max_jerk;</div><div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;        inertia_ = inertia;</div><div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;    }</div><div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;</div><div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;</div><div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;    <span class="keywordtype">double</span> get_safe_torque(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; torque,</div><div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;                           <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; velocity,</div><div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;                           <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; position)</div><div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    {</div><div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;        <span class="keywordtype">double</span> safe_torque = mct::clamp(torque, -max_torque_, max_torque_);</div><div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;</div><div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;safe_torque: &quot; &lt;&lt; safe_torque &lt;&lt; std::endl;</span></div><div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;</div><div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;</div><div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;        <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> max_achievable_acc = max_torque_ / inertia_;</div><div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;</div><div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;</div><div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;</div><div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;</div><div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;        <span class="keywordtype">double</span> max_admissible_acc =</div><div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;                <a class="code" href="dynamical__systems_8hpp.html#aab449f0863dee56d0f0e377c75a4812d">find_max_admissible_acceleration</a>(velocity,</div><div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;                                                 position,</div><div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;                                                 max_velocity_,</div><div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;                                                 max_position_,</div><div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;                                                 max_jerk_,</div><div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;                                                 max_achievable_acc);</div><div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;        <span class="keywordtype">double</span> max_admissible_torque = max_admissible_acc * inertia_;</div><div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;</div><div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;</div><div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;</div><div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;<span class="comment">//        LinearDynamicsWithAccelerationConstraint</span></div><div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;<span class="comment">//                test_dynamics(- max_jerk_,</span></div><div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;<span class="comment">//                              max_achievable_acc,</span></div><div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;<span class="comment">//                              velocity,</span></div><div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="comment">//                              position,</span></div><div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;<span class="comment">//                              max_achievable_acc);</span></div><div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;</div><div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;<span class="comment">//        test_dynamics.print_parameters();</span></div><div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;will exceed: &quot; &lt;&lt; test_dynamics.will_exceed_jointly(max_velocity_, max_position_) &lt;&lt; std::endl;</span></div><div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;max_admissible_acc: &quot; &lt;&lt; max_admissible_acc &lt;&lt; std::endl;</span></div><div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;</div><div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;</div><div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;max_achievable_acc: &quot; &lt;&lt; max_achievable_acc &lt;&lt; std::endl;</span></div><div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;max_admissible_acc: &quot; &lt;&lt; max_admissible_acc &lt;&lt; std::endl;</span></div><div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;max_admissible_torque: &quot; &lt;&lt; max_admissible_torque &lt;&lt; std::endl;</span></div><div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;</div><div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;</div><div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;</div><div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;        <span class="keywordtype">double</span> min_admissible_acc =</div><div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;                find_min_admissible_acceleration(velocity,</div><div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;                                                 position,</div><div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;                                                 min_velocity_,</div><div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;                                                 min_position_,</div><div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;                                                 max_jerk_,</div><div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;                                                 max_achievable_acc);</div><div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;        <span class="keywordtype">double</span> min_admissible_torque = min_admissible_acc * inertia_;</div><div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;</div><div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;min_admissible_acc: &quot; &lt;&lt; min_admissible_acc &lt;&lt; std::endl;</span></div><div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;<span class="comment">//        std::cout &lt;&lt; &quot;min_admissible_torque: &quot; &lt;&lt; min_admissible_torque &lt;&lt; std::endl;</span></div><div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;</div><div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;</div><div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;</div><div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;        <span class="keywordflow">if</span>(min_admissible_torque &gt; max_admissible_torque)</div><div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;        {</div><div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;min_admissible_torque &gt; max_admissible_torque!!!!&quot;</span></div><div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;                      &lt;&lt; std::endl;</div><div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;            <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;        }</div><div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;</div><div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;        safe_torque = mct::clamp(safe_torque,</div><div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;                            min_admissible_torque, max_admissible_torque);</div><div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;</div><div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;</div><div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;        <span class="keywordflow">if</span>(safe_torque &gt; max_torque_ || safe_torque &lt; -max_torque_)</div><div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;        {</div><div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;something went horribly horribly wrong &quot;</span> &lt;&lt; std::endl;</div><div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;            <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;        }</div><div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;</div><div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;        <span class="keywordflow">return</span> safe_torque;</div><div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;    }</div><div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;</div><div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;    <span class="keywordtype">double</span> min_velocity_;</div><div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;    <span class="keywordtype">double</span> min_position_;</div><div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    <span class="keywordtype">double</span> max_velocity_;</div><div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    <span class="keywordtype">double</span> max_position_;</div><div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;    <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> max_torque_;</div><div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;    <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> max_jerk_;</div><div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    <a class="code" href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a> inertia_;</div><div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;};</div><div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;</div><div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;</div><div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;</div><div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;}</div><div class="ttc" id="namespacemct_html"><div class="ttname"><a href="namespacemct.html">mct</a></div><div class="ttdef"><b>Definition:</b> basic_tools.hpp:14</div></div>
<div class="ttc" id="dynamical__systems_8hpp_html_aab449f0863dee56d0f0e377c75a4812d"><div class="ttname"><a href="dynamical__systems_8hpp.html#aab449f0863dee56d0f0e377c75a4812d">mct::find_max_admissible_acceleration</a></div><div class="ttdeci">double find_max_admissible_acceleration(const double &amp;initial_velocity, const double &amp;initial_position, const double &amp;max_velocity, const double &amp;max_position, const mct::NonnegDouble &amp;abs_jerk_limit, const mct::NonnegDouble &amp;abs_acceleration_limit)</div><div class="ttdef"><b>Definition:</b> dynamical_systems.hpp:387</div></div>
<div class="ttc" id="classmct_1_1LinearDynamics_html"><div class="ttname"><a href="classmct_1_1LinearDynamics.html">mct::LinearDynamics</a></div><div class="ttdef"><b>Definition:</b> dynamical_systems.hpp:28</div></div>
<div class="ttc" id="classmct_1_1LinearDynamicsWithAccelerationConstraint_html_a568991a3b2459be274a86298caf8356c"><div class="ttname"><a href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html#a568991a3b2459be274a86298caf8356c">mct::LinearDynamicsWithAccelerationConstraint::will_exceed_jointly</a></div><div class="ttdeci">bool will_exceed_jointly(const double &amp;max_velocity, const double &amp;max_position, double &amp;certificate_time) const </div><div class="ttdef"><b>Definition:</b> dynamical_systems.hpp:281</div></div>
<div class="ttc" id="classmct_1_1NonnegDouble_html"><div class="ttname"><a href="classmct_1_1NonnegDouble.html">mct::NonnegDouble</a></div><div class="ttdef"><b>Definition:</b> basic_tools.hpp:17</div></div>
<div class="ttc" id="math_8hpp_html"><div class="ttname"><a href="math_8hpp.html">math.hpp</a></div></div>
<div class="ttc" id="basic__tools_8hpp_html"><div class="ttname"><a href="basic__tools_8hpp.html">basic_tools.hpp</a></div></div>
<div class="ttc" id="classmct_1_1SafetyConstraint_html"><div class="ttname"><a href="classmct_1_1SafetyConstraint.html">mct::SafetyConstraint</a></div><div class="ttdef"><b>Definition:</b> dynamical_systems.hpp:455</div></div>
<div class="ttc" id="classmct_1_1LinearDynamicsWithAccelerationConstraint_html"><div class="ttname"><a href="classmct_1_1LinearDynamicsWithAccelerationConstraint.html">mct::LinearDynamicsWithAccelerationConstraint</a></div><div class="ttdef"><b>Definition:</b> dynamical_systems.hpp:123</div></div>
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